Re: Converting the integral of a sum into a sum of integrals

*To*: mathgroup at smc.vnet.net*Subject*: [mg109147] Re: Converting the integral of a sum into a sum of integrals*From*: Roland Franzius <roland.franzius at uos.de>*Date*: Mon, 19 Apr 2010 04:11:37 -0400 (EDT)*References*: <201004110831.EAA06714@smc.vnet.net> <hputps$lhj$1@smc.vnet.net>

Kurt TeKolste schrieb: > If I ask Mathematica to perform an indefinite integrate on a symbolic > summation (with terms of the form a_i x^i), > > Integrate[Sum[Times[Power[x,i],Subscript[a,i]],{i,0,k}], > > it does nothing. If I try to tell it that summation and integration > commute by applying the rule: > > Integrate[Sum[term_,range_],variable_]-> > Sum[Integrate[term_,variable_],range_] > > I get a strange result equivalent to > > term * range meaning that Integrate does not see term dependent on variable > > or, in this case, > > Times[Power[x,i],Subscript[a,i]] * {i,0,k} > or > {i a_i x^i, 0, k a_i x^i} > > Any ideas as to what's going on? > > (BTW: > > 1) If you use rules to extract each of term, range, and variable and > then take Sum[Integral[...],...] the correct answer is returned. > > 2) if you use a rule that changes Sum to Power, i.e. > > Integrate[Sum[term_,range_],variable_] -> > Product[Integrate[term_,variable_],range_] > > you get exponents > > term^(range - 1) > > Odd... > ) > > ekt > Use rules that hold its pattern form unevaluated. HoldPattern preserves execution of the first argument of RuleDelayed at any stage of the defining or execution process. Using RuleDelayed (:> )instead of Rule (->) delays evaluation of its second argument to the time of applying the rule in a Replace (/.) -- Roland Franzius rule = HoldPattern[Integrate[Sum[expression_,j_],x_] :> Sum[Integrate[expression,x],j]

**References**:**Re: Symplify Table***From:*Murray Eisenberg <murray@math.umass.edu>